aboutsummaryrefslogtreecommitdiff
path: root/NaturalTransformation/Instance/EmptyMultiset.agda
diff options
context:
space:
mode:
Diffstat (limited to 'NaturalTransformation/Instance/EmptyMultiset.agda')
-rw-r--r--NaturalTransformation/Instance/EmptyMultiset.agda34
1 files changed, 34 insertions, 0 deletions
diff --git a/NaturalTransformation/Instance/EmptyMultiset.agda b/NaturalTransformation/Instance/EmptyMultiset.agda
new file mode 100644
index 0000000..bfec451
--- /dev/null
+++ b/NaturalTransformation/Instance/EmptyMultiset.agda
@@ -0,0 +1,34 @@
+{-# OPTIONS --without-K --safe #-}
+
+open import Level using (Level; _⊔_)
+
+module NaturalTransformation.Instance.EmptyMultiset {c ℓ : Level} where
+
+import Function.Construct.Constant as Const
+
+open import Categories.NaturalTransformation using (NaturalTransformation; ntHelper)
+open import Categories.Functor using (Functor)
+open import Data.Setoid.Unit {c} {c ⊔ ℓ} using (⊤ₛ)
+open import Categories.Functor.Construction.Constant using (const)
+open import Data.Opaque.Multiset using (Multisetₛ; []ₛ; mapₛ)
+open import Functor.Instance.Multiset {c} {ℓ} using (Multiset)
+open import Function.Construct.Constant using () renaming (function to Const)
+open import Relation.Binary using (Setoid)
+open import Data.Setoid using (_⇒ₛ_)
+open import Function using (Func; _⟶ₛ_)
+open import Function.Construct.Setoid using (_∙_)
+
+opaque
+ unfolding mapₛ
+ map-[]ₛ
+ : {A B : Setoid c ℓ}
+ → (f : A ⟶ₛ B)
+ → (open Setoid (⊤ₛ ⇒ₛ Multisetₛ B))
+ → []ₛ ≈ mapₛ f ∙ []ₛ
+ map-[]ₛ {B = B} f = Setoid.refl (Multisetₛ B)
+
+⊤⇒[] : NaturalTransformation (const ⊤ₛ) Multiset
+⊤⇒[] = ntHelper record
+ { η = λ X → []ₛ {Aₛ = X}
+ ; commute = map-[]ₛ
+ }